"It means that our state supports us," one member of a same-sex civil union says

Several same-sex couples came together in the first minutes of New Year's Day in Honolulu to become the first in the state's history to enter into civil unions.

"We really don't want to wait any longer because we have been together for 33 years waiting for the opportunity and our rights and everything that goes with it," said Donna Gedge, who was with her partner Monica Montgomery, speaking to CNN affiliate KITV. "So why wait?"

The couple told CNN last week about their plans to stay up late for the ceremony.

With Hawaii and Delaware joining the list Sunday, five states now recognize same-sex civil unions, while six other states and Washington, D.C., allow same-sex marriage, according to the National Conference of State Legislatures.

Marriage licenses are given to same-sex couples in Massachusetts, Connecticut, Iowa, Vermont, New Hampshire, New York and the District of Columbia, the NCSL says.

California does not currently allow same-sex marriages to be performed.

In May 2008, the state's Supreme Court ruled that same-sex couples have the right to marry in California. Proposition 8, a state constitutional amendment defining marriage as between a man and a woman, passed later that year.

In 2010, a federal district judge ruled that Proposition 8 violated the U.S. Constitution, but enforcement of that decision was stayed pending appeal.

Delaware said its new law became effective at 10 a.m. Sunday.

In Hawaii, online application for civil union licenses was made available beginning at midnight, despite the fact that government offices are closed until Tuesday, the state government said.

The union becomes valid after a ceremony performed by someone licensed by the Department of Health.

"It means that our state supports us, and that's a really good feeling after all this time," Montgomery said at the ceremony.

The laws in Delaware and Hawaii followed heated debates in both states.

In 2010, then-Gov. Linda Lingle, a Republican, vetoed a similar bill in Hawaii, saying the issue needed to be put to a referendum.

Some religious groups were among those pushing for the move. "We need you to mount a campaign to flood the governor's office with requests to veto the bill," Larry Silva, Catholic bishop of Honolulu, wrote on the Diocese of Honolulu's website at the time.

A group called the Hawaii Family Forum argued that "a vote for civil unions is a vote for same-sex marriage."

"Civil unions are a desperate and dishonest attempt to force same-sex 'marriage' on Hawaii," the group said. Despite the opposition, there was no referendum.

In both Hawaii and Delaware, the language of the law emphasizes that "it is not the legislature's intent to revise the definition or eligibility requirements of marriage."

Gedge and Montgomery told CNN last week they hope there will one day be federally recognized same-sex marriage.

Hawaii Gov. Neil Abercrombie, a Democrat, signed the state's civil unions bill into law last February, calling it "a prime example of exercising civic courage. It is about doing what is right, no matter how difficult, no matter how much opposition."

Delaware Gov. Jack Markell, a Democrat, signed his state's bill into law in May.

The Delaware Family Policy Council, which says its goal is to "educate, equip, unify and engage the citizens of Delaware in advocating for family values and preserving the integrity of the family as an institution," argued that civil unions "are a springboard to redefining marriage."

"You can't really talk about civil unions without talking about same-sex 'marriage' because there really isn't any difference," the group argued.

But Markell, at a signing ceremony last year, said, "This bill is about a new energy and excitement. It's about a moment in our history that came about because people came together to work for it, because it became clear that Delaware's LGBT (lesbian, gay, bisexual and transgender) community is in fact part of every Delaware community. The greater good is served when we speak out and fight hard when we see that bias, prejudice or even outdated laws attempt to lessen any one of us."

Bonnie Limatoc, who was part of the midnight ceremony in Hawaii on Sunday, told KITV, "The historic part for me is to be one of the first to open that door so that the rest of them after us, there's others out there that want to do this. ... We can show them, "Hey, you love somebody, you have the right to be with them the rest of your life also.'"

"Our message is go for the gusto," her partner Lydia Pontin added. "Don't be ashamed."